Document Type
Article
Publication Date
6-1-2018
Abstract
We present a model and discretization that couples the Ericksen model of liquid crystals with variable degree of orientation to the Allen–Cahn equations with a mass constraint. The coupled system models liquid crystal droplets with anisotropic surface tension effects due to the liquid crystal molecular alignment. The total energy consists of the Ericksen energy, phase-field (Allen–Cahn) energy, and a weak anchoring energy that couples the liquid crystal to the diffuse interface. We describe our discretization of the total energy along with a method to compute minimizers via a discrete gradient flow algorithm which has a strictly monotone energy decreasing property. Numerical experiments are given in three dimensions that illustrate a wide variety of droplet shapes that result from their interaction with defects.
Publication Source (Journal or Book title)
Computers and Mathematics with Applications
First Page
4048
Last Page
4065
Recommended Citation
Morvant, A., Seal, E., & Walker, S. (2018). A coupled Ericksen/Allen–Cahn model for liquid crystal droplets. Computers and Mathematics with Applications, 75 (11), 4048-4065. https://doi.org/10.1016/j.camwa.2018.03.013